Question
On what sum of money will the difference between the compound interest and simple interest for 2years be equal to Rs 25 if the rate of interest charged for both is 5% p.a.
Use the formula of compound interest and simple interest to get the principal amount.
The correct answer is: Rs 10000
Complete step by step solution:
Let the principal amount = P
It is given that the rate of interest R = 5% and number of years T = 2 years.
So, compound interest for 2 years =
Simple interest
for 2 years =
It is given that compound interest - simple interest = 25 Rupees
That is, Rupees.
Hence the principal amount = Rs 10000
Hence the principal amount = Rs 10000
On what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum be equal to Rs. 63 ?
A. Rs. 24600
B. Rs. 24800
C. Rs. 25200
D. Rs. 25500
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\text{Rate of interest = 5}}\% {\text{ per annum}} \cr & {\text{Time = 2 year}} \cr & {\text{Accroding to question,}} \cr & \Rightarrow P\left[ {{{\left( {1 + \frac{r}{{100}}} \right)}^n} - 1} \right] - \frac{{P \times r \times t}}{{100}}{\text{ = 63}} \cr & \Rightarrow P\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^2} - 1} \right] - \frac{{P \times 5 \times 2}}{{100}}{\text{ = 63}} \cr & \Rightarrow P\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^2} - 1} \right] - \frac{{10P}}{{100}}{\text{ = 63}} \cr & \Rightarrow P\left[ {{{\left( {\frac{{105}}{{100}}} \right)}^2} - 1} \right] - \frac{{10P}}{{100}}{\text{ = 63}} \cr & \Rightarrow P\left( {\frac{{11025 - 10000}}{{10000}}} \right) - \frac{{10P}}{{100}} = 63 \cr & \Rightarrow \frac{{1025P}}{{10000}} - \frac{{10P}}{{100}} = 63 \cr & \Rightarrow \frac{{1025P - 1000P}}{{10000}} = 63 \cr & \Rightarrow 25P = Rs.630000 \cr & \Rightarrow P = \frac{{630000}}{{25}} \cr & \Rightarrow P = Rs. 25200 \cr & {\text{Hence}},\,{\text{sum Rs}}{\text{. 25200}} \cr} $$
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On what sum of money will the difference between the compound interest and simple interest for 2 years be equal to Rs. 25 if the rate of interest charged for both is 5% p.a.?
Solution
C.I = `P[(1 + r/100)^2 - 1] = P[(1 + 5/100)^2 - 1] = "41P"/400`
`S.I = (P xx 5 xx 2)/100 = P/100`
Given, C.I. - S.I. Rs. 25
`=> "41P"/400 - P/10 = 25`
`=> (41P - 40P)/400 = 25`
`=> P = 10000`
∴ Required sum = Rs. 10,000
Concept: Concept of Compound Interest - Compound Interest as a Repeated Simple Interest Computation with a Growing Principal
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